Efficient Algorithms for the Inclusion of the Preisach Hysteresis Model in Nonlinear Finite-Element Methods

This paper deals with key problems that have been commonly encountered in the implementation of the Preisach model into finite-element (FE) programs. Such problems include the inverse problem imposed by certain FE formulations, the abundance use of experimental data needed for identification, and the complex hysteretic nonlinearity inherited in electromagnetic problems. The aim is to alleviate these problems using new efficient algorithms to facilitate the inclusion of the Preisach model in FE equations. The inversion of the model is evaded by systematically creating an inverted Everett function identified from a few parameters usually provided by the makers of electrical steel. The Everett function and its derivatives are ensured to be smooth and continuous by using cubic spline interpolation, which is important for producing stable iterative solutions in the FE computations. Thorough investigations and FE simulations supported by experiments show that the proposed algorithms are capable of successfully accomplishing good accuracy, fast computation, and numerical convergence.